Analytical solutions and moment analysis of general rate model for linear liquid chromatography

Abstract

The general rate model (GRM) is considered to be a comprehensive and reliable mathematical model for describing the separation and mass transfer processes of solutes in chromatographic columns. However, the numerical solution of model equations is complicated and time consuming. This paper presents analytical solutions of the GRM for linear adsorption isotherms and different sets of boundary conditions at the column inlet and outlet. The analytical solutions are obtained by means of Laplace transformation. Numerical Laplace inversion is used to transform back the solution in the time domain because analytical inversion cannot be obtained. The first four temporal moments are derived analytically using the Laplace domain solutions. The moments of GRM are utilized to analyze the retention times, band broadenings, front asymmetries and kurtosis of the

Linear general rate model of chromatography for core–shell particles: Analytical solutions and moment analysis

“…(18) of Qamar et al (2014). Similarly, the other moments of this manuscript reduces to the corresponding moments presented in Appendix B of Qamar et al (2014). The moment expressions derived also reduce correctly into other known results of reduced models, e.g., if k ext goes to infinity, see e.g.…”

“…(15) and B. (18) of Qamar et al (2014). Similarly, the other moments of this manuscript reduces to the corresponding moments presented in Appendix B of Qamar et al (2014).…”

“…(53) for ρ core ¼ 1 and ρ mod ¼ 1 is identical to the well-known equation for fully porous particles after back transforming the time coordinate, see e.g. Guiochon et al (2006) and Qamar et al (2014). Eqs.…”

Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

“…for columns packed with fully porous particles. [20][21][22] Recently, we have also derived analytical solutions and moments of the linear GRM for core-shell particles. [23] In all these derivations, the Laplace transformation was applied as a basic tool to derive analytical solutions.…”

Analysis of general rate model of linear chromatography considering finite rates of the adsorption and desorption steps

“…The analytical solutions of different chromatographic models in the Laplace domain have been recently derived considering the assumption of a linear isotherm, see e.g. Felinger and Guiochon (2004); Javeed et al (2013); Miyabe (2014); Qamar et al (2014Qamar et al ( , 2015. When the Laplace transform is applied in terms of time variable, a function of time is transformed into a function of complex frequency.…”